MinT - Best Known (127, 127+113, s)-Nets in Base 4

Best Known (127, 127+113, s)-Nets in Base 4

(127, 127+113, 130)-Net over F₄ — Constructive and digital

Digital (127, 240, 130)-net over F₄, using

t-expansion [i] based on digital (105, 240, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(127, 127+113, 204)-Net over F₄ — Digital

Digital (127, 240, 204)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+113, 2639)-Net in Base 4 — Upper bound on s

There is no (127, 240, 2640)-net in base 4, because

1 times m-reduction [i] would yield (127, 239, 2640)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 786402 090547 199077 524341 101644 834809 428998 623204 102623 210157 789175 360323 987781 441119 051447 539864 268479 716821 093138 631990 618006 242196 406241 202700 > 4²³⁹ [i]